"We can only apologise to Youssoufa Moukoko for what fans shouted during the Under-19 game," Schalke said on Twitter. "Putting emotions of a derby aside, we fully condemn such insults and reject them."
"We will take the necessary measures together with the Schalke fan department."
The Cameroon-born Moukoko, considered one of the biggest talents in Germany, scored all the goals in their 3-2 win over Schalke on Sunday, with a few fans shouting insults at the teenager, who ignored them.
Moukoko is eligible to compete in the Bundesliga after he turns 16 in November.